that is a linear egr valve. if it malfunctions it will throw a code for egr flow. but there is no way to check it without a 5 gas analyzer and a scanner that will command it to turn on and off. it sounds like the lower intake manifold is leaking that is what happens to almost every 3.1 put out by general motors. 15 years experience as a diagnostic tech. used to work at the chevy dealer as the lead tech.
the vacuum being fine and throttle body being ok still does not rule out an intake gasket leak. the lower intake on those leak oil and coolant into the combustion chamber and externally in small amounts. but another common problem is the ignition module which is under the coil packs. it could be getting hot and cutting out due to a short. you need to check the spark and if it is weak once warm then change the ignition module and coil packs. Another common problem is the fuel pump. how new is the fuel filter and what is your fuel pressure. it needs to be within spec. if it is even 2 lbs low it will cause drive ability problems.
